The following exercise and, um, solution come from Cambridge’s *Mathematical Methods 3 & 4* (2019):

## Update

Reflecting on the comments below, it was a mistake to characterise this exercise as a PoSWW; the exercise had a point that we had missed. The point was to reinforce the Magrittesque lunacy inherent in Methods, and the exercise has done so admirably. The fact that the suggested tangents to the pictured graphs are not parallel adds a special Methodsy charm.

My initial reaction is that this is just completely question-begging. Any competent student would wonder why they should accept that the tangents are parallel, without knowing that the derivatives are equal.

A picture is worth a thousand words. But in this case, it’s worth nine useless words.

It’s a real shame, because there’s value in getting a student to sketch both graphs on the same set of axes in order to test a students understanding of their relative positions. And why one appears to always be above the other is worth asking from a transformations point of view. And using transformations, the question of why the derivatives are the same is trivially explainable.

The “… use them …”part of the question is a wasted opportunity. But the worst part, as implied SRK above, is the unwanted reinforcement of the ‘assumptions based on pictures constitute a proof’ fallacy that is so common among students (and, apparently, also authors of textbooks).

Thanks, John. I agree. There’s clear value in considering function y = log(5x), and the valid arguments for why it is parallel to y = log(x). But, Methods is as Methods does.

Yes, SRK. It would be impossible to make a question more ass-backwards if one tried.